When California came after me for Hawaii income, all I had to do was send them a copy of my Hawaii returns. Someone who lives in NJ will file taxes there anyway.
It’s unclear at this point whether New Jersey will let New York claim all this taxable income or whether New Jersey will try to claim it for itself (it needs the money too). The tax rates are pretty similar in both states but my preference would be for the money to go to the state I actually live in.
And NY will demand their taxes 100%.